Mixture-Coupling theory: a mathematical model of coupled dual chemical osmosis and sorption

Very low permeability geomaterials have been used widely as barriers for landfill or nuclear waste disposal. Such materials can act as an actual semipermeable membrane. Most recently, chemical osmosis & thermal osmosis have been found important in such membrane porous media, but the theoretical and mathematical development remains a challenge due to the complexity of couplings of multiple phases and components, which thereby presents a significant bundle for scientific understanding and engineering application. This paper provides a mathematical model for dual chemical osmosis and chemical reaction based on mixture coupling theory, extending Darcy’s law with chemical osmosis and reaction. The modified Darcy’s law can be applied in any chemical disturbed underground zone.